1. Field of the invention
This invention relates to a frequency characteristic adjusting circuit which is capable of setting the frequency characteristic of phase or amplification (or attenuation) degree.
2. Description of the Prior Art
The transfer function T(s) of a frequency characteristic adjusting circuit having such a frequency characteristic (second-order type) as shown in FIG. 1 can be expressed by ##EQU1## The transfer function T(s) of a band-pass filter having such a frequency characteristic (second-order type), as shown in FIG. 1 can be expressed by ##EQU2## where .omega..sub.0 is the angular velocity of the resonance frequency of the filter and .DELTA..omega. is the band width of the resonance characteristic of the filter.
The angular velocity of an input signal is represented by .omega., and it is set that S=j.omega.. As is well-known, the equation (1) shows the transfer function of a band-eliminate filter or band-pass filter in dependence on whether A=0 or B=0.
To obtain the transfer function of the equation (1), use has been made of such a circuit as illustrated in FIG. 3. In FIG. 3, reference numerals 1 and 2 indicate amplifiers, and 3 designates a band-pass filter. However, the band-pass filter heretofore employed is such a dual-slope integration type circuit (biquad circuit) as depicted in FIG. 4 and hence is very complicated in construction. In FIG. 4, reference numeral 4 identifies an adder; 5 and 6 denote integrators; and 7 and 8 represent feedback circuits.
The dual-slope integration type circuit (biquad circuit) has such a construction as shown in FIG. 4 in which the adder 4 and the integrators 5 and 6 are connected in series, and the outputs from the integrators 5 and 6 are positively and negatively fed back via the feedback circuits 8 and 7 respectively to yield a desired output at an output terminal 9 connected to the integrator 5; namely, this circuit has complexity in construction, involving two such feedback circuits.
A method that has been employed for obtaining the transfer function of the equation (2) is to utilize the resonance characteristic of LC; but it is difficult to independently control Q representing the sharpness of a resonance circuit. With the abovesaid dual-slope integration type circuit (biquad circuit), the resonance frequency or Q can be controlled independently, but a very complicated circuit construction is needed therefor.
Letting the transfer function of a second-order type phase shifter be represented by T(S), it is given by ##EQU3## .omega..sub.0 is the angular velocity of a center frequency, where a is a coefficient, .omega. is the angular velocity of an input signal and S=j.omega.. The frequency characteristic in this case is shown in FIG. 5. FIGS. 5A, B and C respectively show the amplification degree, phase and delay time with respect to the angular velocity .omega..
In the above equation, a phase characteristic P(.omega.) is as follows: ##EQU4## and a group delay characteristic t(.omega.) is as follows: ##EQU5##
Accordingly, a maximum delay t.sub.max occurs when .omega.=.omega..sub.0 and becomes as follows: ##EQU6## Therefore, in the case of the second-order type, the maximum delay t.sub.max can independently be changed relative to the angular velocity .omega..sub.0 at the center frequency, by changing the coefficient a independently. However, known phase shifters having the second-order type transfer function, such as the Dellyannis type and the Moschytz type, are complicated in construction, and it is very difficult to change the center frequency and the maximum delay t.sub.max independently of each other.
The transfer function T(s) of a frequency characteristic adjusting circuit having such frequency characteristics as shown in FIGS. 15A, B and C is expressed by ##EQU7## where .omega..sub.0 is the angular velocity of the resonance frequency of the filter and .DELTA..omega. is the band width of the resonance characteristic of the filter. Further, the angular velocity of an input signal is represented by .omega., and S=j.omega..
The equations (101) and (102) may also be normalized, with ##EQU8## as follows: ##EQU9## In the above, A, B and K are constants, and as is well-known, T(s) indicates a band-eliminate filter or a band-pass filter in dependence on whether A=0 or B=0, as shown in FIG. 1.
It has conventionally been regarded as difficult to obtain a frequency characteristic adjusting circuit having such a transfer function, and the frequency characteristic adjusting circuit has been put into use only in the case K=1, that is, in such a case as depicted in FIG. 15C; also in this case, a complicated circuit arrangement is required.